Modulation instability in higher-order nonlinear Schrödinger equations

Chowdury, Amdad; Ankiewicz, Adrian; Akhmediev, Nail; Chang, Wonkeun

doi:10.1063/1.5053941

Cited by 12 publications

(6 citation statements)

References 72 publications

(120 reference statements)

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“…In principle, infinitely many higher-order terms can be added to the NLSE in such a way that the corresponding equation remains integrable [39][40][41][42]. Despite being cumbersome, these extensions admit exact solutions.…”

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confidence: 99%

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Exact Analytic Spectra of Asymmetric Modulation Instability in Systems with Self-Steepening Effect

Liu

Chen

et al. 2021

Phys. Rev. Lett.

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confidence: 99%

“…Despite being cumbersome, these extensions admit exact solutions. Some extensions of the infinite hierarchy like Hirota or Sasa-Satsuma equations result in the skewed MI dynamics, although many others keep them symmetric [42].…”

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confidence: 99%

Exact Analytic Spectra of Asymmetric Modulation Instability in Systems with Self-Steepening Effect

Liu

Chen

et al. 2021

Phys. Rev. Lett.

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“…It is observed as the millimetric droplet walking on the surface of vibrating fluids, where the motion of droplets is affected by the resonant interaction with their own wave field [40,41]. Systems of the walking droplets demonstrate various quantum effects [42][43][44].…”

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confidence: 99%

Two-fluid hydrodynamics of cold atomic bosons under the influence of quantum fluctuations at non-zero temperatures

Andreev¹

2022

Phys. Scr.

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Ultracold Bose atoms is the physical system existing at the small finite temperatures, where the quantum and nonlinear phenomena play crucial role. Bosons are considered to be composed of two different fluids: the Bose-Einstein condensate and the normal fluid (the thermal component). The extended hydrodynamic models are obtained for each fluids, where the pressure evolution equations and the pressure flux third rank tensor evolution equations are obtained along with the continuity and Euler equations. It is found that the pressure evolution equation contains zero contribution of the short-range interaction. The pressure flux evolution equation contains the interaction which simplifies to the quantum fluctuations in the zero temperature limit. The structure of the third rank tensor describing this interaction is obtained in the regime of small temperature and weak interaction. The model is derived via the straightforward calculation of evolution of macroscopic functions using the microscopic many-particle Schrodinger equation in the coordinate representation. Finally, the two-fluid hydrodynamics is constructed in form of four equations for each fluid in order to give model describing the quantum fluctuations in BEC and the thermal effects in the normal fluid.

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“…It is observed as the millimetric droplet walking on the surface of vibrating fluids, where the motion of droplets is affected by the resonant interaction with their own wave field [37], [38]. Systems walking droplets demonstrate various quantum effects [39], [40], [41].…”

Section: B the Pressure Evolution Equationmentioning

confidence: 99%

Two-fluid hydrodynamics of cold atomic bosons under influence of the quantum fluctuations at non-zero temperatures

Andreev¹

2021

Preprint

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Ultracold Bose atoms is the physical system, where the quantum and nonlinear phenomena play crucial role. Ultracold bosons are considered at the small finite temperatures. Bosons are considered as two different fluids: Bose-Einstein condensate and normal fluid (the thermal component). An extended hydrodynamic model is obtained for both fluids, where the pressure evolution equations and the pressure flux third rank tensor evolution equations are considered along with the continuity and Euler equations. It is found that the pressure evolution equation contains zero contribution of the short-range interaction. The pressure flux evolution equation contains the interaction which gives the quantum fluctuations in the zero temperature limit. Here, we obtain its generalization for the finite temperature. The contribution of interaction in the pressure flux evolution equation which goes to zero in the zero temperature limit is found. The model is obtained via the straightforward derivation from the microscopic many-particle Schrodinger equation in the coordinate representation.

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Modulation instability in higher-order nonlinear Schrödinger equations

Cited by 12 publications

References 72 publications

Exact Analytic Spectra of Asymmetric Modulation Instability in Systems with Self-Steepening Effect

Exact Analytic Spectra of Asymmetric Modulation Instability in Systems with Self-Steepening Effect

Two-fluid hydrodynamics of cold atomic bosons under the influence of quantum fluctuations at non-zero temperatures

Two-fluid hydrodynamics of cold atomic bosons under influence of the quantum fluctuations at non-zero temperatures

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